Because of different behavior of reservoir water and dam material, the determination of hydrodynamic pressure during earthquake is very complicated. Thus, different formulations have been presented for modeling of the dam reservoir system under dynamic loading such as earthquake. These formulations can be categorized into two general groups, which are Lagrangian and Eulerian, each having advantages and disadvantages. In this paper, a proper formulation is presented for modeling of reservoir of concrete dams and determination of the hydrodynamic pressure based on finite element, and the Lagrangian and Eulerian methods. The Lagrangian and Eulerian methods are then compared with together for the determination of hydrodynamic pressure on the dam upstream and the displacement of the crest of dam for a variety of dimensions of dam under different types of earthquake. The results brought up from these two formulations are then compared with each other in different aspects such as accuracy, the required amount of calculations, the frequency effect, the boundary conditions, the dam upstream slope, the sediment in energy absorption, the reservoir height and its bed slope and eventually, the type of elements used in finite element method.
Furthermore, the formulation of reservoir using Lagrangian method for applying boundary conditions as especial element has been used and the results show that this method is an improvement of the existing finite element method in comparison with usual Lagrangian method in other to decrease the degree of freedom.